Implement Sliding Windows and Fit a Polynomial

# -*- coding=UTF-8 -*-
import numpy as np
import cv2
import matplotlib.pyplot as plt
import matplotlib.image as mapping

binary_warped = mapping.imread("warped.jpg")
plt.figure(figsize=(12,12))
plt.imshow(binary_warped,cmap="gray") # 二值图像要用cmap关键字指定图像格式
plt.plot(100,300,"*r") # 坐标原点位于左上角，x为水平向右，y为水平向下
# img = np.zeros_like(binary_warped)
# img = np.dstack((img,img,img))
# cv2.rectangle(img,(100,200),(200,500),(0,255,0),3)
# plt.imshow(img,cmap="gray")

[<matplotlib.lines.Line2D at 0x23a5be47eb8>]

# Take a histogram of the bottom half of the image
histogram = np.sum(binary_warped[binary_warped.shape[0]//2:,:], axis=0)
# Create an output image to draw on and  visualize the result
out_img = np.dstack((binary_warped, binary_warped, binary_warped))*255
# Find the peak of the left and right halves of the histogram
# These will be the starting point for the left and right lines
midpoint = np.int(histogram.shape[0]//2)
leftx_base = np.argmax(histogram[:midpoint])
rightx_base = np.argmax(histogram[midpoint:]) + midpoint

# Choose the number of sliding windows
nwindows = 9
# Set height of windows
window_height = np.int(binary_warped.shape[0]//nwindows)
# Identify the x and y positions of all nonzero pixels in the image
nonzero = binary_warped.nonzero() # 返回非零元素的索引(index_rows,index_cols)
nonzeroy = np.array(nonzero[0])
nonzerox = np.array(nonzero[1])
# Current positions to be updated for each window
leftx_current = leftx_base
rightx_current = rightx_base
# Set the width of the windows +/- margin
margin = 100
# Set minimum number of pixels found to recenter window
minpix = 50
# Create empty lists to receive left and right lane pixel indices
left_lane_inds = []
right_lane_inds = []

# Step through the windows one by one
for window in range(nwindows):
    # Identify window boundaries in x and y (and right and left)
    win_y_low = binary_warped.shape[0] - (window+1)*window_height   # 矩形上边
    win_y_high = binary_warped.shape[0] - window*window_height      # 矩形下边
    win_xleft_low = leftx_current - margin    # 左矩形左边
    win_xleft_high = leftx_current + margin   # 左矩形右边
    win_xright_low = rightx_current - margin  # 右矩形左边
    win_xright_high = rightx_current + margin # 右矩形右边
    # Draw the windows on the visualization image
    cv2.rectangle(out_img,(win_xleft_low,win_y_low),(win_xleft_high,win_y_high),(0,255,0), 2) # 左上角，右下角坐标；线颜色
    cv2.rectangle(out_img,(win_xright_low,win_y_low),(win_xright_high,win_y_high),(0,255,0), 2) 
    # Identify the nonzero pixels in x and y within the window
    good_left_inds = ((nonzeroy >= win_y_low) & (nonzeroy < win_y_high) & (nonzerox >= win_xleft_low) &  
                      (nonzerox < win_xleft_high)).nonzero()[0] # 左边框里的像素索引
    good_right_inds = ((nonzeroy >= win_y_low) & (nonzeroy < win_y_high) & (nonzerox >= win_xright_low) &  
                       (nonzerox < win_xright_high)).nonzero()[0] # 右边框力度像素索引
    # Append these indices to the lists
    left_lane_inds.append(good_left_inds) # 逐个将9个边框中的索引加入list中
    right_lane_inds.append(good_right_inds)
    # If you found > minpix pixels, recenter next window on their mean position
    if len(good_left_inds) > minpix:
        leftx_current = np.int(np.mean(nonzerox[good_left_inds]))
    if len(good_right_inds) > minpix:        
        rightx_current = np.int(np.mean(nonzerox[good_right_inds]))

# Concatenate the arrays of indices
left_lane_inds = np.concatenate(left_lane_inds) # 将9个拼起来的list合成一个
right_lane_inds = np.concatenate(right_lane_inds)

# Extract left and right line pixel positions
leftx = nonzerox[left_lane_inds]
lefty = nonzeroy[left_lane_inds] 
rightx = nonzerox[right_lane_inds]
righty = nonzeroy[right_lane_inds] 

# Fit a second order polynomial to each
left_fit = np.polyfit(lefty, leftx, 2) # 求二阶矩方程的系数，这里注意y在前，x在后，因为有共同的y轴
right_fit = np.polyfit(righty, rightx, 2)

Visualization

# Generate x and y values for plotting
ploty = np.linspace(0, binary_warped.shape[0]-1, binary_warped.shape[0] )
left_fitx = left_fit[0]*ploty**2 + left_fit[1]*ploty + left_fit[2]
right_fitx = right_fit[0]*ploty**2 + right_fit[1]*ploty + right_fit[2]

out_img[nonzeroy[left_lane_inds], nonzerox[left_lane_inds]] = [255, 0, 0]
out_img[nonzeroy[right_lane_inds], nonzerox[right_lane_inds]] = [0, 0, 255]
plt.figure(figsize=(12,12))
plt.imshow(out_img)
plt.plot(left_fitx, ploty, color='yellow')
plt.plot(right_fitx, ploty, color='yellow')
plt.xlim(0, 1280)
plt.ylim(720, 0)

(720, 0)

Skip the sliding windows step once you know where the lines are

# It's now much easier to find line pixels!
nonzero = binary_warped.nonzero()
nonzeroy = np.array(nonzero[0])
nonzerox = np.array(nonzero[1])
margin = 100
left_lane_inds = ((nonzerox > (left_fit[0]*(nonzeroy**2) + left_fit[1]*nonzeroy + left_fit[2] - margin)) & 
                  (nonzerox < (left_fit[0]*(nonzeroy**2) + left_fit[1]*nonzeroy + left_fit[2] + margin))) # 距离左拟合线左右±100的点

right_lane_inds = ((nonzerox > (right_fit[0]*(nonzeroy**2) + right_fit[1]*nonzeroy + right_fit[2] - margin)) & 
                   (nonzerox < (right_fit[0]*(nonzeroy**2) + right_fit[1]*nonzeroy + right_fit[2] + margin)))  # 距离右拟合线左右±100的点

# Again, extract left and right line pixel positions
leftx = nonzerox[left_lane_inds]
lefty = nonzeroy[left_lane_inds] 
rightx = nonzerox[right_lane_inds]
righty = nonzeroy[right_lane_inds]
# Fit a second order polynomial to each
left_fit = np.polyfit(lefty, leftx, 2)
right_fit = np.polyfit(righty, rightx, 2)
# Generate x and y values for plotting
ploty = np.linspace(0, binary_warped.shape[0]-1, binary_warped.shape[0] )
left_fitx = left_fit[0]*ploty**2 + left_fit[1]*ploty + left_fit[2]
right_fitx = right_fit[0]*ploty**2 + right_fit[1]*ploty + right_fit[2]

# Create an image to draw on and an image to show the selection window
out_img = np.dstack((binary_warped, binary_warped, binary_warped))*255
window_img = np.zeros_like(out_img)
# Color in left and right line pixels
out_img[nonzeroy[left_lane_inds], nonzerox[left_lane_inds]] = [255, 0, 0]
out_img[nonzeroy[right_lane_inds], nonzerox[right_lane_inds]] = [0, 0, 255]

# Generate a polygon to illustrate the search window area
# And recast the x and y points into usable format for cv2.fillPoly()
left_line_window1 = np.array([np.transpose(np.vstack([left_fitx-margin, ploty]))]) # 左车道线左100处所有点的坐标
left_line_window2 = np.array([np.flipud(np.transpose(np.vstack([left_fitx+margin, ploty])))]) # 左车道线右100处所有点的坐标
left_line_pts = np.hstack((left_line_window1, left_line_window2))
right_line_window1 = np.array([np.transpose(np.vstack([right_fitx-margin, ploty]))]) # 右车道线左100处所有点的坐标
right_line_window2 = np.array([np.flipud(np.transpose(np.vstack([right_fitx+margin,  ploty])))]) # 右车道线右100处所有点的坐标
right_line_pts = np.hstack((right_line_window1, right_line_window2))

# Draw the lane onto the warped blank image
cv2.fillPoly(window_img, np.int_([left_line_pts]), (0,255, 0))
cv2.fillPoly(window_img, np.int_([right_line_pts]), (0,255, 0))
result = cv2.addWeighted(out_img, 1, window_img, 0.3, 0)
plt.figure(figsize=(12,12))
plt.imshow(result)
plt.plot(left_fitx, ploty, color='yellow')
plt.plot(right_fitx, ploty, color='yellow')
plt.xlim(0, 1280)
plt.ylim(720, 0)

(720, 0)

The Method of Convolution

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.image as mpimg
import glob
import cv2

# Read in a thresholded image
warped = mpimg.imread('warped.jpg')
# window settings
window_width = 50 
window_height = 80 # Break image into 9 vertical layers since image height is 720
margin = 100 # How much to slide left and right for searching

def window_mask(width, height, img_ref, center,level):
    output = np.zeros_like(img_ref)
    output[int(img_ref.shape[0]-(level+1)*height):int(img_ref.shape[0]-level*height),max(0,int(center-width/2)):min(int(center+width/2),img_ref.shape[1])] = 1
    return output

def find_window_centroids(image, window_width, window_height, margin):  
    window_centroids = [] # Store the (left,right) window centroid positions per level
    window = np.ones(window_width) # Create our window template that we will use for convolutions
    
    # First find the two starting positions for the left and right lane by using np.sum to get the vertical image slice
    # and then np.convolve the vertical image slice with the window template 
    
    # Sum quarter bottom of image to get slice, could use a different ratio
    l_sum = np.sum(image[int(3*image.shape[0]/4):,:int(image.shape[1]/2)], axis=0)
    l_center = np.argmax(np.convolve(window,l_sum))-window_width/2
    r_sum = np.sum(image[int(3*image.shape[0]/4):,int(image.shape[1]/2):], axis=0)
    r_center = np.argmax(np.convolve(window,r_sum))-window_width/2+int(image.shape[1]/2)
    
    # Add what we found for the first layer
    window_centroids.append((l_center,r_center))
    
    # Go through each layer looking for max pixel locations
    for level in range(1,(int)(image.shape[0]/window_height)):
        # convolve the window into the vertical slice of the image
        image_layer = np.sum(image[int(image.shape[0]-(level+1)*window_height):int(image.shape[0]-level*window_height),:], axis=0)
        conv_signal = np.convolve(window, image_layer)
        # Find the best left centroid by using past left center as a reference
        # Use window_width/2 as offset because convolution signal reference is at right side of window, not center of window
        offset = window_width/2
        l_min_index = int(max(l_center+offset-margin,0))
        l_max_index = int(min(l_center+offset+margin,image.shape[1]))
        l_center = np.argmax(conv_signal[l_min_index:l_max_index])+l_min_index-offset
        # Find the best right centroid by using past right center as a reference
        r_min_index = int(max(r_center+offset-margin,0))
        r_max_index = int(min(r_center+offset+margin,image.shape[1]))
        r_center = np.argmax(conv_signal[r_min_index:r_max_index])+r_min_index-offset
        # Add what we found for that layer
        window_centroids.append((l_center,r_center))

    return window_centroids

window_centroids = find_window_centroids(warped, window_width, window_height, margin)

# If we found any window centers
if len(window_centroids) > 0:
    # Points used to draw all the left and right windows
    l_points = np.zeros_like(warped)
    r_points = np.zeros_like(warped)

    # Go through each level and draw the windows 	
    for level in range(0,len(window_centroids)):
        # Window_mask is a function to draw window areas
        l_mask = window_mask(window_width,window_height,warped,window_centroids[level][0],level)
        r_mask = window_mask(window_width,window_height,warped,window_centroids[level][1],level)
        # Add graphic points from window mask here to total pixels found 
        l_points[(l_points == 255) | ((l_mask == 1) ) ] = 255
        r_points[(r_points == 255) | ((r_mask == 1) ) ] = 255

    # Draw the results
    template = np.array(r_points+l_points,np.uint8) # add both left and right window pixels together
    zero_channel = np.zeros_like(template) # create a zero color channel
    template = np.array(cv2.merge((zero_channel,template,zero_channel)),np.uint8) # make window pixels green
    warpage= np.dstack((warped, warped, warped))*255 # making the original road pixels 3 color channels
    output = cv2.addWeighted(warpage, 1, template, 0.5, 0.0) # overlay the orignal road image with window results

else: # If no window centers found, just display orginal road image
    output = np.array(cv2.merge((warped,warped,warped)),np.uint8)

# Display the final results
plt.figure(figsize=(12,12))
plt.imshow(output)
plt.title('window fitting results')
plt.show()